/*
   As part of the ccal program by Zhuo Meng, this version is
   distributed under the terms of the GNU Lesser General Public License as
   published by the Free Software Foundation; either version 2 of the
   License, or (at your option) any later version.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public License
   along with this program; if not, write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

   The whole package can be obtained from
   http://aa.usno.navy.mil/software/novas/novas_c/novasc_info.php

   Adapted from:

   Naval Observatory Vector Astrometry Software (NOVAS)
   C Edition, Version 3.1
   
   nutation.c: Nutation models

   U. S. Naval Observatory
   Astronomical Applications Dept.
   Washington, DC 
   http://www.usno.navy.mil/USNO/astronomical-applications
*/

#ifndef _NOVAS_
   #include "novas.h"
#endif

/********iau2000a */

void iau2000a (double jd_high, double jd_low,

               double *dpsi, double *deps)
/*
------------------------------------------------------------------------

   PURPOSE:
      To compute the forced nutation of the non-rigid Earth based on
      the IAU 2000A nutation model.

   REFERENCES:
      IERS Conventions (2003), Chapter 5.
      Simon et al. (1994) Astronomy and Astrophysics 282, 663-683,
         esp. Sections 3.4-3.5.

   INPUT
   ARGUMENTS:
      jd_high (double)
         High-order part of TT Julian date.
      jd_low (double)
         Low-order part of TT Julian date.

   OUTPUT
   ARGUMENTS:
      *dpsi (double)
         Nutation (luni-solar + planetary) in longitude, in radians.
      *deps (double)
         Nutation (luni-solar + planetary) in obliquity, in radians.

   RETURNED
   VALUE:
      None.

   GLOBALS
   USED:
      T0, ASEC2RAD, TWOPI

   FUNCTIONS
   CALLED:
      fund_args    novas.c
      fmod         math.h
      sin          math.h
      cos          math.h

   VER./DATE/
   PROGRAMMER:
      V1.0/03-04/JAB (USNO/AA)
      V1.1/12-10/JAB (USNO/AA): Implement static storage class for const
                                arrays.
      V1.2/03-11/WKP (USNO/AA): Added braces to 2-D array initialization
                                to quiet gcc warnings.

   NOTES:
     1. The IAU 2000A nutation model is MHB_2000 without the free core
     nutation and without the corrections to Lieske precession.
     2. This function is the "C" version of NOVAS Fortran routine
     'nu2000a'.

------------------------------------------------------------------------
*/
{
   short int i;

   double t, a[5], dp, de, arg, sarg, carg, factor, dpsils, depsls,
      al, alsu, af, ad, aom, alme, alve, alea, alma, alju, alsa, alur,
      alne, apa, dpsipl, depspl;

/*
   Luni-Solar argument multipliers:
       L     L'    F     D     Om
*/

   static const short int nals_t[678][5] = {
      { 0,    0,    0,    0,    1},
      { 0,    0,    2,   -2,    2},
      { 0,    0,    2,    0,    2},
      { 0,    0,    0,    0,    2},
      { 0,    1,    0,    0,    0},
      { 0,    1,    2,   -2,    2},
      { 1,    0,    0,    0,    0},
      { 0,    0,    2,    0,    1},
      { 1,    0,    2,    0,    2},
      { 0,   -1,    2,   -2,    2},
      { 0,    0,    2,   -2,    1},
      {-1,    0,    2,    0,    2},
      {-1,    0,    0,    2,    0},
      { 1,    0,    0,    0,    1},
      {-1,    0,    0,    0,    1},
      {-1,    0,    2,    2,    2},
      { 1,    0,    2,    0,    1},
      {-2,    0,    2,    0,    1},
      { 0,    0,    0,    2,    0},
      { 0,    0,    2,    2,    2},
      { 0,   -2,    2,   -2,    2},
      {-2,    0,    0,    2,    0},
      { 2,    0,    2,    0,    2},
      { 1,    0,    2,   -2,    2},
      {-1,    0,    2,    0,    1},
      { 2,    0,    0,    0,    0},
      { 0,    0,    2,    0,    0},
      { 0,    1,    0,    0,    1},
      {-1,    0,    0,    2,    1},
      { 0,    2,    2,   -2,    2},
      { 0,    0,   -2,    2,    0},
      { 1,    0,    0,   -2,    1},
      { 0,   -1,    0,    0,    1},
      {-1,    0,    2,    2,    1},
      { 0,    2,    0,    0,    0},
      { 1,    0,    2,    2,    2},
      {-2,    0,    2,    0,    0},
      { 0,    1,    2,    0,    2},
      { 0,    0,    2,    2,    1},
      { 0,   -1,    2,    0,    2},
      { 0,    0,    0,    2,    1},
      { 1,    0,    2,   -2,    1},
      { 2,    0,    2,   -2,    2},
      {-2,    0,    0,    2,    1},
      { 2,    0,    2,    0,    1},
      { 0,   -1,    2,   -2,    1},
      { 0,    0,    0,   -2,    1},
      {-1,   -1,    0,    2,    0},
      { 2,    0,    0,   -2,    1},
      { 1,    0,    0,    2,    0},
      { 0,    1,    2,   -2,    1},
      { 1,   -1,    0,    0,    0},
      {-2,    0,    2,    0,    2},
      { 3,    0,    2,    0,    2},
      { 0,   -1,    0,    2,    0},
      { 1,   -1,    2,    0,    2},
      { 0,    0,    0,    1,    0},
      {-1,   -1,    2,    2,    2},
      {-1,    0,    2,    0,    0},
      { 0,   -1,    2,    2,    2},
      {-2,    0,    0,    0,    1},
      { 1,    1,    2,    0,    2},
      { 2,    0,    0,    0,    1},
      {-1,    1,    0,    1,    0},
      { 1,    1,    0,    0,    0},
      { 1,    0,    2,    0,    0},
      {-1,    0,    2,   -2,    1},
      { 1,    0,    0,    0,    2},
      {-1,    0,    0,    1,    0},
      { 0,    0,    2,    1,    2},
      {-1,    0,    2,    4,    2},
      {-1,    1,    0,    1,    1},
      { 0,   -2,    2,   -2,    1},
      { 1,    0,    2,    2,    1},
      {-2,    0,    2,    2,    2},
      {-1,    0,    0,    0,    2},
      { 1,    1,    2,   -2,    2},
      {-2,    0,    2,    4,    2},
      {-1,    0,    4,    0,    2},
      { 2,    0,    2,   -2,    1},
      { 2,    0,    2,    2,    2},
      { 1,    0,    0,    2,    1},
      { 3,    0,    0,    0,    0},
      { 3,    0,    2,   -2,    2},
      { 0,    0,    4,   -2,    2},
      { 0,    1,    2,    0,    1},
      { 0,    0,   -2,    2,    1},
      { 0,    0,    2,   -2,    3},
      {-1,    0,    0,    4,    0},
      { 2,    0,   -2,    0,    1},
      {-2,    0,    0,    4,    0},
      {-1,   -1,    0,    2,    1},
      {-1,    0,    0,    1,    1},
      { 0,    1,    0,    0,    2},
      { 0,    0,   -2,    0,    1},
      { 0,   -1,    2,    0,    1},
      { 0,    0,    2,   -1,    2},
      { 0,    0,    2,    4,    2},
      {-2,   -1,    0,    2,    0},
      { 1,    1,    0,   -2,    1},
      {-1,    1,    0,    2,    0},
      {-1,    1,    0,    1,    2},
      { 1,   -1,    0,    0,    1},
      { 1,   -1,    2,    2,    2},
      {-1,    1,    2,    2,    2},
      { 3,    0,    2,    0,    1},
      { 0,    1,   -2,    2,    0},
      {-1,    0,    0,   -2,    1},
      { 0,    1,    2,    2,    2},
      {-1,   -1,    2,    2,    1},
      { 0,   -1,    0,    0,    2},
      { 1,    0,    2,   -4,    1},
      {-1,    0,   -2,    2,    0},
      { 0,   -1,    2,    2,    1},
      { 2,   -1,    2,    0,    2},
      { 0,    0,    0,    2,    2},
      { 1,   -1,    2,    0,    1},
      {-1,    1,    2,    0,    2},
      { 0,    1,    0,    2,    0},
      { 0,   -1,   -2,    2,    0},
      { 0,    3,    2,   -2,    2},
      { 0,    0,    0,    1,    1},
      {-1,    0,    2,    2,    0},
      { 2,    1,    2,    0,    2},
      { 1,    1,    0,    0,    1},
      { 1,    1,    2,    0,    1},
      { 2,    0,    0,    2,    0},
      { 1,    0,   -2,    2,    0},
      {-1,    0,    0,    2,    2},
      { 0,    1,    0,    1,    0},
      { 0,    1,    0,   -2,    1},
      {-1,    0,    2,   -2,    2},
      { 0,    0,    0,   -1,    1},
      {-1,    1,    0,    0,    1},
      { 1,    0,    2,   -1,    2},
      { 1,   -1,    0,    2,    0},
      { 0,    0,    0,    4,    0},
      { 1,    0,    2,    1,    2},
      { 0,    0,    2,    1,    1},
      { 1,    0,    0,   -2,    2},
      {-1,    0,    2,    4,    1},
      { 1,    0,   -2,    0,    1},
      { 1,    1,    2,   -2,    1},
      { 0,    0,    2,    2,    0},
      {-1,    0,    2,   -1,    1},
      {-2,    0,    2,    2,    1},
      { 4,    0,    2,    0,    2},
      { 2,   -1,    0,    0,    0},
      { 2,    1,    2,   -2,    2},
      { 0,    1,    2,    1,    2},
      { 1,    0,    4,   -2,    2},
      {-1,   -1,    0,    0,    1},
      { 0,    1,    0,    2,    1},
      {-2,    0,    2,    4,    1},
      { 2,    0,    2,    0,    0},
      { 1,    0,    0,    1,    0},
      {-1,    0,    0,    4,    1},
      {-1,    0,    4,    0,    1},
      { 2,    0,    2,    2,    1},
      { 0,    0,    2,   -3,    2},
      {-1,   -2,    0,    2,    0},
      { 2,    1,    0,    0,    0},
      { 0,    0,    4,    0,    2},
      { 0,    0,    0,    0,    3},
      { 0,    3,    0,    0,    0},
      { 0,    0,    2,   -4,    1},
      { 0,   -1,    0,    2,    1},
      { 0,    0,    0,    4,    1},
      {-1,   -1,    2,    4,    2},
      { 1,    0,    2,    4,    2},
      {-2,    2,    0,    2,    0},
      {-2,   -1,    2,    0,    1},
      {-2,    0,    0,    2,    2},
      {-1,   -1,    2,    0,    2},
      { 0,    0,    4,   -2,    1},
      { 3,    0,    2,   -2,    1},
      {-2,   -1,    0,    2,    1},
      { 1,    0,    0,   -1,    1},
      { 0,   -2,    0,    2,    0},
      {-2,    0,    0,    4,    1},
      {-3,    0,    0,    0,    1},
      { 1,    1,    2,    2,    2},
      { 0,    0,    2,    4,    1},
      { 3,    0,    2,    2,    2},
      {-1,    1,    2,   -2,    1},
      { 2,    0,    0,   -4,    1},
      { 0,    0,    0,   -2,    2},
      { 2,    0,    2,   -4,    1},
      {-1,    1,    0,    2,    1},
      { 0,    0,    2,   -1,    1},
      { 0,   -2,    2,    2,    2},
      { 2,    0,    0,    2,    1},
      { 4,    0,    2,   -2,    2},
      { 2,    0,    0,   -2,    2},
      { 0,    2,    0,    0,    1},
      { 1,    0,    0,   -4,    1},
      { 0,    2,    2,   -2,    1},
      {-3,    0,    0,    4,    0},
      {-1,    1,    2,    0,    1},
      {-1,   -1,    0,    4,    0},
      {-1,   -2,    2,    2,    2},
      {-2,   -1,    2,    4,    2},
      { 1,   -1,    2,    2,    1},
      {-2,    1,    0,    2,    0},
      {-2,    1,    2,    0,    1},
      { 2,    1,    0,   -2,    1},
      {-3,    0,    2,    0,    1},
      {-2,    0,    2,   -2,    1},
      {-1,    1,    0,    2,    2},
      { 0,   -1,    2,   -1,    2},
      {-1,    0,    4,   -2,    2},
      { 0,   -2,    2,    0,    2},
      {-1,    0,    2,    1,    2},
      { 2,    0,    0,    0,    2},
      { 0,    0,    2,    0,    3},
      {-2,    0,    4,    0,    2},
      {-1,    0,   -2,    0,    1},
      {-1,    1,    2,    2,    1},
      { 3,    0,    0,    0,    1},
      {-1,    0,    2,    3,    2},
      { 2,   -1,    2,    0,    1},
      { 0,    1,    2,    2,    1},
      { 0,   -1,    2,    4,    2},
      { 2,   -1,    2,    2,    2},
      { 0,    2,   -2,    2,    0},
      {-1,   -1,    2,   -1,    1},
      { 0,   -2,    0,    0,    1},
      { 1,    0,    2,   -4,    2},
      { 1,   -1,    0,   -2,    1},
      {-1,   -1,    2,    0,    1},
      { 1,   -1,    2,   -2,    2},
      {-2,   -1,    0,    4,    0},
      {-1,    0,    0,    3,    0},
      {-2,   -1,    2,    2,    2},
      { 0,    2,    2,    0,    2},
      { 1,    1,    0,    2,    0},
      { 2,    0,    2,   -1,    2},
      { 1,    0,    2,    1,    1},
      { 4,    0,    0,    0,    0},
      { 2,    1,    2,    0,    1},
      { 3,   -1,    2,    0,    2},
      {-2,    2,    0,    2,    1},
      { 1,    0,    2,   -3,    1},
      { 1,    1,    2,   -4,    1},
      {-1,   -1,    2,   -2,    1},
      { 0,   -1,    0,   -1,    1},
      { 0,   -1,    0,   -2,    1},
      {-2,    0,    0,    0,    2},
      {-2,    0,   -2,    2,    0},
      {-1,    0,   -2,    4,    0},
      { 1,   -2,    0,    0,    0},
      { 0,    1,    0,    1,    1},
      {-1,    2,    0,    2,    0},
      { 1,   -1,    2,   -2,    1},
      { 1,    2,    2,   -2,    2},
      { 2,   -1,    2,   -2,    2},
      { 1,    0,    2,   -1,    1},
      { 2,    1,    2,   -2,    1},
      {-2,    0,    0,   -2,    1},
      { 1,   -2,    2,    0,    2},
      { 0,    1,    2,    1,    1},
      { 1,    0,    4,   -2,    1},
      {-2,    0,    4,    2,    2},
      { 1,    1,    2,    1,    2},
      { 1,    0,    0,    4,    0},
      { 1,    0,    2,    2,    0},
      { 2,    0,    2,    1,    2},
      { 3,    1,    2,    0,    2},
      { 4,    0,    2,    0,    1},
      {-2,   -1,    2,    0,    0},
      { 0,    1,   -2,    2,    1},
      { 1,    0,   -2,    1,    0},
      { 0,   -1,   -2,    2,    1},
      { 2,   -1,    0,   -2,    1},
      {-1,    0,    2,   -1,    2},
      { 1,    0,    2,   -3,    2},
      { 0,    1,    2,   -2,    3},
      { 0,    0,    2,   -3,    1},
      {-1,    0,   -2,    2,    1},
      { 0,    0,    2,   -4,    2},
      {-2,    1,    0,    0,    1},
      {-1,    0,    0,   -1,    1},
      { 2,    0,    2,   -4,    2},
      { 0,    0,    4,   -4,    4},
      { 0,    0,    4,   -4,    2},
      {-1,   -2,    0,    2,    1},
      {-2,    0,    0,    3,    0},
      { 1,    0,   -2,    2,    1},
      {-3,    0,    2,    2,    2},
      {-3,    0,    2,    2,    1},
      {-2,    0,    2,    2,    0},
      { 2,   -1,    0,    0,    1},
      {-2,    1,    2,    2,    2},
      { 1,    1,    0,    1,    0},
      { 0,    1,    4,   -2,    2},
      {-1,    1,    0,   -2,    1},
      { 0,    0,    0,   -4,    1},
      { 1,   -1,    0,    2,    1},
      { 1,    1,    0,    2,    1},
      {-1,    2,    2,    2,    2},
      { 3,    1,    2,   -2,    2},
      { 0,   -1,    0,    4,    0},
      { 2,   -1,    0,    2,    0},
      { 0,    0,    4,    0,    1},
      { 2,    0,    4,   -2,    2},
      {-1,   -1,    2,    4,    1},
      { 1,    0,    0,    4,    1},
      { 1,   -2,    2,    2,    2},
      { 0,    0,    2,    3,    2},
      {-1,    1,    2,    4,    2},
      { 3,    0,    0,    2,    0},
      {-1,    0,    4,    2,    2},
      { 1,    1,    2,    2,    1},
      {-2,    0,    2,    6,    2},
      { 2,    1,    2,    2,    2},
      {-1,    0,    2,    6,    2},
      { 1,    0,    2,    4,    1},
      { 2,    0,    2,    4,    2},
      { 1,    1,   -2,    1,    0},
      {-3,    1,    2,    1,    2},
      { 2,    0,   -2,    0,    2},
      {-1,    0,    0,    1,    2},
      {-4,    0,    2,    2,    1},
      {-1,   -1,    0,    1,    0},
      { 0,    0,   -2,    2,    2},
      { 1,    0,    0,   -1,    2},
      { 0,   -1,    2,   -2,    3},
      {-2,    1,    2,    0,    0},
      { 0,    0,    2,   -2,    4},
      {-2,   -2,    0,    2,    0},
      {-2,    0,   -2,    4,    0},
      { 0,   -2,   -2,    2,    0},
      { 1,    2,    0,   -2,    1},
      { 3,    0,    0,   -4,    1},
      {-1,    1,    2,   -2,    2},
      { 1,   -1,    2,   -4,    1},
      { 1,    1,    0,   -2,    2},
      {-3,    0,    2,    0,    0},
      {-3,    0,    2,    0,    2},
      {-2,    0,    0,    1,    0},
      { 0,    0,   -2,    1,    0},
      {-3,    0,    0,    2,    1},
      {-1,   -1,   -2,    2,    0},
      { 0,    1,    2,   -4,    1},
      { 2,    1,    0,   -4,    1},
      { 0,    2,    0,   -2,    1},
      { 1,    0,    0,   -3,    1},
      {-2,    0,    2,   -2,    2},
      {-2,   -1,    0,    0,    1},
      {-4,    0,    0,    2,    0},
      { 1,    1,    0,   -4,    1},
      {-1,    0,    2,   -4,    1},
      { 0,    0,    4,   -4,    1},
      { 0,    3,    2,   -2,    2},
      {-3,   -1,    0,    4,    0},
      {-3,    0,    0,    4,    1},
      { 1,   -1,   -2,    2,    0},
      {-1,   -1,    0,    2,    2},
      { 1,   -2,    0,    0,    1},
      { 1,   -1,    0,    0,    2},
      { 0,    0,    0,    1,    2},
      {-1,   -1,    2,    0,    0},
      { 1,   -2,    2,   -2,    2},
      { 0,   -1,    2,   -1,    1},
      {-1,    0,    2,    0,    3},
      { 1,    1,    0,    0,    2},
      {-1,    1,    2,    0,    0},
      { 1,    2,    0,    0,    0},
      {-1,    2,    2,    0,    2},
      {-1,    0,    4,   -2,    1},
      { 3,    0,    2,   -4,    2},
      { 1,    2,    2,   -2,    1},
      { 1,    0,    4,   -4,    2},
      {-2,   -1,    0,    4,    1},
      { 0,   -1,    0,    2,    2},
      {-2,    1,    0,    4,    0},
      {-2,   -1,    2,    2,    1},
      { 2,    0,   -2,    2,    0},
      { 1,    0,    0,    1,    1},
      { 0,    1,    0,    2,    2},
      { 1,   -1,    2,   -1,    2},
      {-2,    0,    4,    0,    1},
      { 2,    1,    0,    0,    1},
      { 0,    1,    2,    0,    0},
      { 0,   -1,    4,   -2,    2},
      { 0,    0,    4,   -2,    4},
      { 0,    2,    2,    0,    1},
      {-3,    0,    0,    6,    0},
      {-1,   -1,    0,    4,    1},
      { 1,   -2,    0,    2,    0},
      {-1,    0,    0,    4,    2},
      {-1,   -2,    2,    2,    1},
      {-1,    0,    0,   -2,    2},
      { 1,    0,   -2,   -2,    1},
      { 0,    0,   -2,   -2,    1},
      {-2,    0,   -2,    0,    1},
      { 0,    0,    0,    3,    1},
      { 0,    0,    0,    3,    0},
      {-1,    1,    0,    4,    0},
      {-1,   -1,    2,    2,    0},
      {-2,    0,    2,    3,    2},
      { 1,    0,    0,    2,    2},
      { 0,   -1,    2,    1,    2},
      { 3,   -1,    0,    0,    0},
      { 2,    0,    0,    1,    0},
      { 1,   -1,    2,    0,    0},
      { 0,    0,    2,    1,    0},
      { 1,    0,    2,    0,    3},
      { 3,    1,    0,    0,    0},
      { 3,   -1,    2,   -2,    2},
      { 2,    0,    2,   -1,    1},
      { 1,    1,    2,    0,    0},
      { 0,    0,    4,   -1,    2},
      { 1,    2,    2,    0,    2},
      {-2,    0,    0,    6,    0},
      { 0,   -1,    0,    4,    1},
      {-2,   -1,    2,    4,    1},
      { 0,   -2,    2,    2,    1},
      { 0,   -1,    2,    2,    0},
      {-1,    0,    2,    3,    1},
      {-2,    1,    2,    4,    2},
      { 2,    0,    0,    2,    2},
      { 2,   -2,    2,    0,    2},
      {-1,    1,    2,    3,    2},
      { 3,    0,    2,   -1,    2},
      { 4,    0,    2,   -2,    1},
      {-1,    0,    0,    6,    0},
      {-1,   -2,    2,    4,    2},
      {-3,    0,    2,    6,    2},
      {-1,    0,    2,    4,    0},
      { 3,    0,    0,    2,    1},
      { 3,   -1,    2,    0,    1},
      { 3,    0,    2,    0,    0},
      { 1,    0,    4,    0,    2},
      { 5,    0,    2,   -2,    2},
      { 0,   -1,    2,    4,    1},
      { 2,   -1,    2,    2,    1},
      { 0,    1,    2,    4,    2},
      { 1,   -1,    2,    4,    2},
      { 3,   -1,    2,    2,    2},
      { 3,    0,    2,    2,    1},
      { 5,    0,    2,    0,    2},
      { 0,    0,    2,    6,    2},
      { 4,    0,    2,    2,    2},
      { 0,   -1,    1,   -1,    1},
      {-1,    0,    1,    0,    3},
      { 0,   -2,    2,   -2,    3},
      { 1,    0,   -1,    0,    1},
      { 2,   -2,    0,   -2,    1},
      {-1,    0,    1,    0,    2},
      {-1,    0,    1,    0,    1},
      {-1,   -1,    2,   -1,    2},
      {-2,    2,    0,    2,    2},
      {-1,    0,    1,    0,    0},
      {-4,    1,    2,    2,    2},
      {-3,    0,    2,    1,    1},
      {-2,   -1,    2,    0,    2},
      { 1,    0,   -2,    1,    1},
      { 2,   -1,   -2,    0,    1},
      {-4,    0,    2,    2,    0},
      {-3,    1,    0,    3,    0},
      {-1,    0,   -1,    2,    0},
      { 0,   -2,    0,    0,    2},
      { 0,   -2,    0,    0,    2},
      {-3,    0,    0,    3,    0},
      {-2,   -1,    0,    2,    2},
      {-1,    0,   -2,    3,    0},
      {-4,    0,    0,    4,    0},
      { 2,    1,   -2,    0,    1},
      { 2,   -1,    0,   -2,    2},
      { 0,    0,    1,   -1,    0},
      {-1,    2,    0,    1,    0},
      {-2,    1,    2,    0,    2},
      { 1,    1,    0,   -1,    1},
      { 1,    0,    1,   -2,    1},
      { 0,    2,    0,    0,    2},
      { 1,   -1,    2,   -3,    1},
      {-1,    1,    2,   -1,    1},
      {-2,    0,    4,   -2,    2},
      {-2,    0,    4,   -2,    1},
      {-2,   -2,    0,    2,    1},
      {-2,    0,   -2,    4,    0},
      { 1,    2,    2,   -4,    1},
      { 1,    1,    2,   -4,    2},
      {-1,    2,    2,   -2,    1},
      { 2,    0,    0,   -3,    1},
      {-1,    2,    0,    0,    1},
      { 0,    0,    0,   -2,    0},
      {-1,   -1,    2,   -2,    2},
      {-1,    1,    0,    0,    2},
      { 0,    0,    0,   -1,    2},
      {-2,    1,    0,    1,    0},
      { 1,   -2,    0,   -2,    1},
      { 1,    0,   -2,    0,    2},
      {-3,    1,    0,    2,    0},
      {-1,    1,   -2,    2,    0},
      {-1,   -1,    0,    0,    2},
      {-3,    0,    0,    2,    0},
      {-3,   -1,    0,    2,    0},
      { 2,    0,    2,   -6,    1},
      { 0,    1,    2,   -4,    2},
      { 2,    0,    0,   -4,    2},
      {-2,    1,    2,   -2,    1},
      { 0,   -1,    2,   -4,    1},
      { 0,    1,    0,   -2,    2},
      {-1,    0,    0,   -2,    0},
      { 2,    0,   -2,   -2,    1},
      {-4,    0,    2,    0,    1},
      {-1,   -1,    0,   -1,    1},
      { 0,    0,   -2,    0,    2},
      {-3,    0,    0,    1,    0},
      {-1,    0,   -2,    1,    0},
      {-2,    0,   -2,    2,    1},
      { 0,    0,   -4,    2,    0},
      {-2,   -1,   -2,    2,    0},
      { 1,    0,    2,   -6,    1},
      {-1,    0,    2,   -4,    2},
      { 1,    0,    0,   -4,    2},
      { 2,    1,    2,   -4,    2},
      { 2,    1,    2,   -4,    1},
      { 0,    1,    4,   -4,    4},
      { 0,    1,    4,   -4,    2},
      {-1,   -1,   -2,    4,    0},
      {-1,   -3,    0,    2,    0},
      {-1,    0,   -2,    4,    1},
      {-2,   -1,    0,    3,    0},
      { 0,    0,   -2,    3,    0},
      {-2,    0,    0,    3,    1},
      { 0,   -1,    0,    1,    0},
      {-3,    0,    2,    2,    0},
      { 1,    1,   -2,    2,    0},
      {-1,    1,    0,    2,    2},
      { 1,   -2,    2,   -2,    1},
      { 0,    0,    1,    0,    2},
      { 0,    0,    1,    0,    1},
      { 0,    0,    1,    0,    0},
      {-1,    2,    0,    2,    1},
      { 0,    0,    2,    0,    2},
      {-2,    0,    2,    0,    2},
      { 2,    0,    0,   -1,    1},
      { 3,    0,    0,   -2,    1},
      { 1,    0,    2,   -2,    3},
      { 1,    2,    0,    0,    1},
      { 2,    0,    2,   -3,    2},
      {-1,    1,    4,   -2,    2},
      {-2,   -2,    0,    4,    0},
      { 0,   -3,    0,    2,    0},
      { 0,    0,   -2,    4,    0},
      {-1,   -1,    0,    3,    0},
      {-2,    0,    0,    4,    2},
      {-1,    0,    0,    3,    1},
      { 2,   -2,    0,    0,    0},
      { 1,   -1,    0,    1,    0},
      {-1,    0,    0,    2,    0},
      { 0,   -2,    2,    0,    1},
      {-1,    0,    1,    2,    1},
      {-1,    1,    0,    3,    0},
      {-1,   -1,    2,    1,    2},
      { 0,   -1,    2,    0,    0},
      {-2,    1,    2,    2,    1},
      { 2,   -2,    2,   -2,    2},
      { 1,    1,    0,    1,    1},
      { 1,    0,    1,    0,    1},
      { 1,    0,    1,    0,    0},
      { 0,    2,    0,    2,    0},
      { 2,   -1,    2,   -2,    1},
      { 0,   -1,    4,   -2,    1},
      { 0,    0,    4,   -2,    3},
      { 0,    1,    4,   -2,    1},
      { 4,    0,    2,   -4,    2},
      { 2,    2,    2,   -2,    2},
      { 2,    0,    4,   -4,    2},
      {-1,   -2,    0,    4,    0},
      {-1,   -3,    2,    2,    2},
      {-3,    0,    2,    4,    2},
      {-3,    0,    2,   -2,    1},
      {-1,   -1,    0,   -2,    1},
      {-3,    0,    0,    0,    2},
      {-3,    0,   -2,    2,    0},
      { 0,    1,    0,   -4,    1},
      {-2,    1,    0,   -2,    1},
      {-4,    0,    0,    0,    1},
      {-1,    0,    0,   -4,    1},
      {-3,    0,    0,   -2,    1},
      { 0,    0,    0,    3,    2},
      {-1,    1,    0,    4,    1},
      { 1,   -2,    2,    0,    1},
      { 0,    1,    0,    3,    0},
      {-1,    0,    2,    2,    3},
      { 0,    0,    2,    2,    2},
      {-2,    0,    2,    2,    2},
      {-1,    1,    2,    2,    0},
      { 3,    0,    0,    0,    2},
      { 2,    1,    0,    1,    0},
      { 2,   -1,    2,   -1,    2},
      { 0,    0,    2,    0,    1},
      { 0,    0,    3,    0,    3},
      { 0,    0,    3,    0,    2},
      {-1,    2,    2,    2,    1},
      {-1,    0,    4,    0,    0},
      { 1,    2,    2,    0,    1},
      { 3,    1,    2,   -2,    1},
      { 1,    1,    4,   -2,    2},
      {-2,   -1,    0,    6,    0},
      { 0,   -2,    0,    4,    0},
      {-2,    0,    0,    6,    1},
      {-2,   -2,    2,    4,    2},
      { 0,   -3,    2,    2,    2},
      { 0,    0,    0,    4,    2},
      {-1,   -1,    2,    3,    2},
      {-2,    0,    2,    4,    0},
      { 2,   -1,    0,    2,    1},
      { 1,    0,    0,    3,    0},
      { 0,    1,    0,    4,    1},
      { 0,    1,    0,    4,    0},
      { 1,   -1,    2,    1,    2},
      { 0,    0,    2,    2,    3},
      { 1,    0,    2,    2,    2},
      {-1,    0,    2,    2,    2},
      {-2,    0,    4,    2,    1},
      { 2,    1,    0,    2,    1},
      { 2,    1,    0,    2,    0},
      { 2,   -1,    2,    0,    0},
      { 1,    0,    2,    1,    0},
      { 0,    1,    2,    2,    0},
      { 2,    0,    2,    0,    3},
      { 3,    0,    2,    0,    2},
      { 1,    0,    2,    0,    2},
      { 1,    0,    3,    0,    3},
      { 1,    1,    2,    1,    1},
      { 0,    2,    2,    2,    2},
      { 2,    1,    2,    0,    0},
      { 2,    0,    4,   -2,    1},
      { 4,    1,    2,   -2,    2},
      {-1,   -1,    0,    6,    0},
      {-3,   -1,    2,    6,    2},
      {-1,    0,    0,    6,    1},
      {-3,    0,    2,    6,    1},
      { 1,   -1,    0,    4,    1},
      { 1,   -1,    0,    4,    0},
      {-2,    0,    2,    5,    2},
      { 1,   -2,    2,    2,    1},
      { 3,   -1,    0,    2,    0},
      { 1,   -1,    2,    2,    0},
      { 0,    0,    2,    3,    1},
      {-1,    1,    2,    4,    1},
      { 0,    1,    2,    3,    2},
      {-1,    0,    4,    2,    1},
      { 2,    0,    2,    1,    1},
      { 5,    0,    0,    0,    0},
      { 2,    1,    2,    1,    2},
      { 1,    0,    4,    0,    1},
      { 3,    1,    2,    0,    1},
      { 3,    0,    4,   -2,    2},
      {-2,   -1,    2,    6,    2},
      { 0,    0,    0,    6,    0},
      { 0,   -2,    2,    4,    2},
      {-2,    0,    2,    6,    1},
      { 2,    0,    0,    4,    1},
      { 2,    0,    0,    4,    0},
      { 2,   -2,    2,    2,    2},
      { 0,    0,    2,    4,    0},
      { 1,    0,    2,    3,    2},
      { 4,    0,    0,    2,    0},
      { 2,    0,    2,    2,    0},
      { 0,    0,    4,    2,    2},
      { 4,   -1,    2,    0,    2},
      { 3,    0,    2,    1,    2},
      { 2,    1,    2,    2,    1},
      { 4,    1,    2,    0,    2},
      {-1,   -1,    2,    6,    2},
      {-1,    0,    2,    6,    1},
      { 1,   -1,    2,    4,    1},
      { 1,    1,    2,    4,    2},
      { 3,    1,    2,    2,    2},
      { 5,    0,    2,    0,    1},
      { 2,   -1,    2,    4,    2},
      { 2,    0,    2,    4,    1}};

/*
   Luni-Solar nutation coefficients, unit 1e-7 arcsec:
   longitude (sin, t*sin, cos), obliquity (cos, t*cos, sin)

   Each row of coefficients in 'cls_t' belongs with the corresponding
   row of fundamental-argument multipliers in 'nals_t'.
*/

   static const double cls_t[678][6] = {
      {-172064161.0, -174666.0,  33386.0, 92052331.0,  9086.0, 15377.0},
      { -13170906.0,   -1675.0, -13696.0,  5730336.0, -3015.0, -4587.0},
      {  -2276413.0,    -234.0,   2796.0,   978459.0,  -485.0,  1374.0},
      {   2074554.0,     207.0,   -698.0,  -897492.0,   470.0,  -291.0},
      {   1475877.0,   -3633.0,  11817.0,    73871.0,  -184.0, -1924.0},
      {   -516821.0,    1226.0,   -524.0,   224386.0,  -677.0,  -174.0},
      {    711159.0,      73.0,   -872.0,    -6750.0,     0.0,   358.0},
      {   -387298.0,    -367.0,    380.0,   200728.0,    18.0,   318.0},
      {   -301461.0,     -36.0,    816.0,   129025.0,   -63.0,   367.0},
      {    215829.0,    -494.0,    111.0,   -95929.0,   299.0,   132.0},
      {    128227.0,     137.0,    181.0,   -68982.0,    -9.0,    39.0},
      {    123457.0,      11.0,     19.0,   -53311.0,    32.0,    -4.0},
      {    156994.0,      10.0,   -168.0,    -1235.0,     0.0,    82.0},
      {     63110.0,      63.0,     27.0,   -33228.0,     0.0,    -9.0},
      {    -57976.0,     -63.0,   -189.0,    31429.0,     0.0,   -75.0},
      {    -59641.0,     -11.0,    149.0,    25543.0,   -11.0,    66.0},
      {    -51613.0,     -42.0,    129.0,    26366.0,     0.0,    78.0},
      {     45893.0,      50.0,     31.0,   -24236.0,   -10.0,    20.0},
      {     63384.0,      11.0,   -150.0,    -1220.0,     0.0,    29.0},
      {    -38571.0,      -1.0,    158.0,    16452.0,   -11.0,    68.0},
      {     32481.0,       0.0,      0.0,   -13870.0,     0.0,     0.0},
      {    -47722.0,       0.0,    -18.0,      477.0,     0.0,   -25.0},
      {    -31046.0,      -1.0,    131.0,    13238.0,   -11.0,    59.0},
      {     28593.0,       0.0,     -1.0,   -12338.0,    10.0,    -3.0},
      {     20441.0,      21.0,     10.0,   -10758.0,     0.0,    -3.0},
      {     29243.0,       0.0,    -74.0,     -609.0,     0.0,    13.0},
      {     25887.0,       0.0,    -66.0,     -550.0,     0.0,    11.0},
      {    -14053.0,     -25.0,     79.0,     8551.0,    -2.0,   -45.0},
      {     15164.0,      10.0,     11.0,    -8001.0,     0.0,    -1.0},
      {    -15794.0,      72.0,    -16.0,     6850.0,   -42.0,    -5.0},
      {     21783.0,       0.0,     13.0,     -167.0,     0.0,    13.0},
      {    -12873.0,     -10.0,    -37.0,     6953.0,     0.0,   -14.0},
      {    -12654.0,      11.0,     63.0,     6415.0,     0.0,    26.0},
      {    -10204.0,       0.0,     25.0,     5222.0,     0.0,    15.0},
      {     16707.0,     -85.0,    -10.0,      168.0,    -1.0,    10.0},
      {     -7691.0,       0.0,     44.0,     3268.0,     0.0,    19.0},
      {    -11024.0,       0.0,    -14.0,      104.0,     0.0,     2.0},
      {      7566.0,     -21.0,    -11.0,    -3250.0,     0.0,    -5.0},
      {     -6637.0,     -11.0,     25.0,     3353.0,     0.0,    14.0},
      {     -7141.0,      21.0,      8.0,     3070.0,     0.0,     4.0},
      {     -6302.0,     -11.0,      2.0,     3272.0,     0.0,     4.0},
      {      5800.0,      10.0,      2.0,    -3045.0,     0.0,    -1.0},
      {      6443.0,       0.0,     -7.0,    -2768.0,     0.0,    -4.0},
      {     -5774.0,     -11.0,    -15.0,     3041.0,     0.0,    -5.0},
      {     -5350.0,       0.0,     21.0,     2695.0,     0.0,    12.0},
      {     -4752.0,     -11.0,     -3.0,     2719.0,     0.0,    -3.0},
      {     -4940.0,     -11.0,    -21.0,     2720.0,     0.0,    -9.0},
      {      7350.0,       0.0,     -8.0,      -51.0,     0.0,     4.0},
      {      4065.0,       0.0,      6.0,    -2206.0,     0.0,     1.0},
      {      6579.0,       0.0,    -24.0,     -199.0,     0.0,     2.0},
      {      3579.0,       0.0,      5.0,    -1900.0,     0.0,     1.0},
      {      4725.0,       0.0,     -6.0,      -41.0,     0.0,     3.0},
      {     -3075.0,       0.0,     -2.0,     1313.0,     0.0,    -1.0},
      {     -2904.0,       0.0,     15.0,     1233.0,     0.0,     7.0},
      {      4348.0,       0.0,    -10.0,      -81.0,     0.0,     2.0},
      {     -2878.0,       0.0,      8.0,     1232.0,     0.0,     4.0},
      {     -4230.0,       0.0,      5.0,      -20.0,     0.0,    -2.0},
      {     -2819.0,       0.0,      7.0,     1207.0,     0.0,     3.0},
      {     -4056.0,       0.0,      5.0,       40.0,     0.0,    -2.0},
      {     -2647.0,       0.0,     11.0,     1129.0,     0.0,     5.0},
      {     -2294.0,       0.0,    -10.0,     1266.0,     0.0,    -4.0},
      {      2481.0,       0.0,     -7.0,    -1062.0,     0.0,    -3.0},
      {      2179.0,       0.0,     -2.0,    -1129.0,     0.0,    -2.0},
      {      3276.0,       0.0,      1.0,       -9.0,     0.0,     0.0},
      {     -3389.0,       0.0,      5.0,       35.0,     0.0,    -2.0},
      {      3339.0,       0.0,    -13.0,     -107.0,     0.0,     1.0},
      {     -1987.0,       0.0,     -6.0,     1073.0,     0.0,    -2.0},
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      {        -4.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -5.0,       0.0,      0.0,        3.0,     0.0,     0.0},
      {       -13.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -7.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        10.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,       -1.0,     0.0,     0.0},
      {        10.0,       0.0,     13.0,        6.0,     0.0,    -5.0},
      {         0.0,       0.0,     30.0,        0.0,     0.0,    14.0},
      {         0.0,       0.0,   -162.0,        0.0,     0.0,  -138.0},
      {         0.0,       0.0,     75.0,        0.0,     0.0,     0.0},
      {        -7.0,       0.0,      0.0,        4.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        -5.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {         6.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         9.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -7.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        1.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {         7.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -6.0,       0.0,     -3.0,        3.0,     0.0,     1.0},
      {         0.0,       0.0,     -3.0,        0.0,     0.0,    -2.0},
      {        11.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,       -1.0,     0.0,     0.0},
      {        11.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        -1.0,       0.0,      3.0,        3.0,     0.0,    -1.0},
      {         4.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {         0.0,       0.0,    -13.0,        0.0,     0.0,   -11.0},
      {         3.0,       0.0,      6.0,        0.0,     0.0,     0.0},
      {        -7.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        1.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {        -7.0,       0.0,      0.0,        3.0,     0.0,     0.0},
      {         8.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        11.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        1.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,       -1.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {         8.0,       0.0,      0.0,       -4.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,       -1.0,     0.0,     0.0},
      {        11.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -6.0,       0.0,      0.0,        3.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        -8.0,       0.0,      0.0,        4.0,     0.0,     0.0},
      {        -7.0,       0.0,      0.0,        3.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,       -1.0,     0.0,     0.0},
      {         6.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {        -6.0,       0.0,      0.0,        3.0,     0.0,     0.0},
      {         6.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         6.0,       0.0,      0.0,       -1.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {        -5.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         6.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {         0.0,       0.0,    -26.0,        0.0,     0.0,   -11.0},
      {         0.0,       0.0,    -10.0,        0.0,     0.0,    -5.0},
      {         5.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {       -13.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {         7.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        -6.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        -5.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        -7.0,       0.0,      0.0,        3.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {        13.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {       -11.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {         6.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {       -12.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,       -1.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        1.0,     0.0,     0.0},
      {         0.0,       0.0,     -5.0,        0.0,     0.0,    -2.0},
      {        -7.0,       0.0,      0.0,        4.0,     0.0,     0.0},
      {         6.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,       -1.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        1.0,     0.0,     0.0},
      {        -5.0,       0.0,      0.0,        3.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        12.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,       -1.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         6.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {        -6.0,       0.0,      0.0,        3.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {         6.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {         6.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -6.0,       0.0,      0.0,        3.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {         7.0,       0.0,      0.0,       -4.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {        -5.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -6.0,       0.0,      0.0,        3.0,     0.0,     0.0},
      {        -6.0,       0.0,      0.0,        3.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        10.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {         7.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         7.0,       0.0,      0.0,       -3.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {        11.0,       0.0,      0.0,        0.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {        -6.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {         5.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        -4.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        2.0,     0.0,     0.0},
      {         4.0,       0.0,      0.0,       -2.0,     0.0,     0.0},
      {         3.0,       0.0,      0.0,       -1.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        1.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        1.0,     0.0,     0.0},
      {        -3.0,       0.0,      0.0,        2.0,     0.0,     0.0}};

/*
   Planetary argument multipliers:
       L   L'  F   D   Om  Me  Ve  E  Ma  Ju  Sa  Ur  Ne  pre
*/
   static const short int napl_t[687][14] = {
      { 0,  0,  0,  0,  0,  0,  0,  8,-16,  4,  5,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  0, -8, 16, -4, -5,  0,  0,  2},
      { 0,  0,  0,  0,  0,  0,  0,  8,-16,  4,  5,  0,  0,  2},
      { 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1,  2,  2},
      { 0,  0,  0,  0,  0,  0,  0, -4,  8, -1, -5,  0,  0,  2},
      { 0,  0,  0,  0,  0,  0,  0,  4, -8,  3,  0,  0,  0,  1},
      { 0,  0,  1, -1,  1,  0,  0,  3, -8,  3,  0,  0,  0,  0},
      {-1,  0,  0,  0,  0,  0, 10, -3,  0,  0,  0,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  0,  0,  0, -2,  6, -3,  0,  2},
      { 0,  0,  0,  0,  0,  0,  0,  4, -8,  3,  0,  0,  0,  0},
      { 0,  0,  1, -1,  1,  0,  0, -5,  8, -3,  0,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  0, -4,  8, -3,  0,  0,  0,  1},
      { 0,  0,  0,  0,  0,  0,  0,  4, -8,  1,  5,  0,  0,  2},
      { 0,  0,  0,  0,  0,  0, -5,  6,  4,  0,  0,  0,  0,  2},
      { 0,  0,  0,  0,  0,  0,  0,  0,  0,  2, -5,  0,  0,  2},
      { 0,  0,  0,  0,  0,  0,  0,  0,  0,  2, -5,  0,  0,  1},
      { 0,  0,  1, -1,  1,  0,  0, -1,  0,  2, -5,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  0,  0,  0,  2, -5,  0,  0,  0},
      { 0,  0,  1, -1,  1,  0,  0, -1,  0, -2,  5,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  0,  0,  0, -2,  5,  0,  0,  1},
      { 0,  0,  0,  0,  0,  0,  0,  0,  0, -2,  5,  0,  0,  2},
      { 2,  0, -1, -1,  0,  0,  0,  3, -7,  0,  0,  0,  0,  0},
      { 1,  0,  0, -2,  0,  0, 19,-21,  3,  0,  0,  0,  0,  0},
      { 0,  0,  1, -1,  1,  0,  2, -4,  0, -3,  0,  0,  0,  0},
      { 1,  0,  0, -1,  1,  0,  0, -1,  0,  2,  0,  0,  0,  0},
      { 0,  0,  1, -1,  1,  0,  0, -1,  0, -4, 10,  0,  0,  0},
      {-2,  0,  0,  2,  1,  0,  0,  2,  0,  0, -5,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  3, -7,  4,  0,  0,  0,  0,  0},
      { 0,  0, -1,  1,  0,  0,  0,  1,  0,  1, -1,  0,  0,  0},
      {-2,  0,  0,  2,  1,  0,  0,  2,  0, -2,  0,  0,  0,  0},
      {-1,  0,  0,  0,  0,  0, 18,-16,  0,  0,  0,  0,  0,  0},
      {-2,  0,  1,  1,  2,  0,  0,  1,  0, -2,  0,  0,  0,  0},
      {-1,  0,  1, -1,  1,  0, 18,-17,  0,  0,  0,  0,  0,  0},
      {-1,  0,  0,  1,  1,  0,  0,  2, -2,  0,  0,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0, -8, 13,  0,  0,  0,  0,  0,  2},
      { 0,  0,  2, -2,  2,  0, -8, 11,  0,  0,  0,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0, -8, 13,  0,  0,  0,  0,  0,  1},
      { 0,  0,  1, -1,  1,  0, -8, 12,  0,  0,  0,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  8,-13,  0,  0,  0,  0,  0,  0},
      { 0,  0,  1, -1,  1,  0,  8,-14,  0,  0,  0,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  8,-13,  0,  0,  0,  0,  0,  1},
      {-2,  0,  0,  2,  1,  0,  0,  2,  0, -4,  5,  0,  0,  0},
      {-2,  0,  0,  2,  2,  0,  3, -3,  0,  0,  0,  0,  0,  0},
      {-2,  0,  0,  2,  0,  0,  0,  2,  0, -3,  1,  0,  0,  0},
      { 0,  0,  0,  0,  1,  0,  3, -5,  0,  2,  0,  0,  0,  0},
      {-2,  0,  0,  2,  0,  0,  0,  2,  0, -4,  3,  0,  0,  0},
      { 0,  0, -1,  1,  0,  0,  0,  0,  2,  0,  0,  0,  0,  0},
      { 0,  0,  0,  0,  1,  0,  0, -1,  2,  0,  0,  0,  0,  0},
      { 0,  0,  1, -1,  2,  0,  0, -2,  2,  0,  0,  0,  0,  0},
      {-1,  0,  1,  0,  1,  0,  3, -5,  0,  0,  0,  0,  0,  0},
      {-1,  0,  0,  1,  0,  0,  3, -4,  0,  0,  0,  0,  0,  0},
      {-2,  0,  0,  2,  0,  0,  0,  2,  0, -2, -2,  0,  0,  0},
      {-2,  0,  2,  0,  2,  0,  0, -5,  9,  0,  0,  0,  0,  0},
      { 0,  0,  1, -1,  1,  0,  0, -1,  0,  0,  0, -1,  0,  0},
      { 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  0,  0},
      { 0,  0,  1, -1,  1,  0,  0, -1,  0,  0,  0,  0,  2,  0},
      { 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  2,  1},
      { 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  2,  2},
      {-1,  0,  0,  1,  0,  0,  0,  3, -4,  0,  0,  0,  0,  0},
      { 0,  0, -1,  1,  0,  0,  0,  1,  0,  0,  2,  0,  0,  0},
      { 0,  0,  1, -1,  2,  0,  0, -1,  0,  0,  2,  0,  0,  0},
      { 0,  0,  0,  0,  1,  0,  0, -9, 17,  0,  0,  0,  0,  0},
      { 0,  0,  0,  0,  2,  0, -3,  5,  0,  0,  0,  0,  0,  0},
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      { 0,  0,  0,  0,  0,  0,  0,  5,  0, -2,  0,  0,  0,  2},
      { 0,  0,  0,  0,  0,  0,  3,  0,  0,  0,  0,  0,  0,  2},
      { 0,  0,  0,  0,  0,  0, -8,  8,  0,  0,  0,  0,  0,  1},
      { 0,  0,  0,  0,  0,  0,  8, -8,  0,  0,  0,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  5, -3,  0,  0,  0,  0,  0,  1},
      { 0,  0,  0,  0,  0,  0,  5, -3,  0,  0,  0,  0,  0,  2},
      { 0,  0,  0,  0,  0,  0, -9,  9,  0,  0,  0,  0,  0,  1},
      { 0,  0,  0,  0,  0,  0, -9,  9,  0,  0,  0,  0,  0,  1},
      { 0,  0,  0,  0,  0,  0, -9,  9,  0,  0,  0,  0,  0,  1},
      { 0,  0,  0,  0,  0,  0,  9, -9,  0,  0,  0,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  6, -4,  0,  0,  0,  0,  0,  1},
      { 0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  2},
      { 0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  1},
      { 0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  2},
      { 0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  1},
      { 0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  2},
      { 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  2},
      { 1,  0,  0, -2,  0,  0,  0,  2,  0, -2,  0,  0,  0,  0},
      { 1,  0,  0, -2,  0,  0,  2, -2,  0,  0,  0,  0,  0,  0},
      { 1,  0,  0, -2,  0,  0,  0,  1,  0, -1,  0,  0,  0,  0},
      { 1,  0,  0, -2,  0,  0,  1, -1,  0,  0,  0,  0,  0,  0},
      {-1,  0,  0,  0,  0,  0,  3, -3,  0,  0,  0,  0,  0,  0},
      {-1,  0,  0,  0,  0,  0,  0,  2,  0, -2,  0,  0,  0,  0},
      {-1,  0,  0,  2,  0,  0,  0,  4, -8,  3,  0,  0,  0,  0},
      { 1,  0,  0, -2,  0,  0,  0,  4, -8,  3,  0,  0,  0,  0},
      {-2,  0,  0,  2,  0,  0,  0,  4, -8,  3,  0,  0,  0,  0},
      {-1,  0,  0,  0,  0,  0,  0,  2,  0, -3,  0,  0,  0,  0},
      {-1,  0,  0,  0,  0,  0,  0,  1,  0, -1,  0,  0,  0,  0},
      {-1,  0,  0,  0,  0,  0,  1, -1,  0,  0,  0,  0,  0,  0},
      {-1,  0,  0,  2,  0,  0,  2, -2,  0,  0,  0,  0,  0,  0},
      { 1,  0, -1,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0},
      {-1,  0,  0,  2,  0,  0,  0,  2,  0, -3,  0,  0,  0,  0},
      {-2,  0,  0,  0,  0,  0,  0,  2,  0, -3,  0,  0,  0,  0},
      { 1,  0,  0,  0,  0,  0,  0,  4, -8,  3,  0,  0,  0,  0},
      {-1,  0,  1, -1,  1,  0,  0, -1,  0,  0,  0,  0,  0,  0},
      { 1,  0,  1, -1,  1,  0,  0, -1,  0,  0,  0,  0,  0,  0},
      {-1,  0,  0,  0,  0,  0,  0,  4, -8,  3,  0,  0,  0,  0},
      {-1,  0,  0,  2,  1,  0,  0,  2,  0, -2,  0,  0,  0,  0},
      { 0,  0,  0,  0,  0,  0,  0,  2,  0, -2,  0,  0,  0,  0},
      {-1,  0,  0,  2,  0,  0,  0,  2,  0, -2,  0,  0,  0,  0},
      {-1,  0,  0,  2,  0,  0,  3, -3,  0,  0,  0,  0,  0,  0},
      { 1,  0,  0, -2,  1,  0,  0, -2,  0,  2,  0,  0,  0,  0},
      { 1,  0,  2, -2,  2,  0, -3,  3,  0,  0,  0,  0,  0,  0},
      { 1,  0,  2, -2,  2,  0,  0, -2,  0,  2,  0,  0,  0,  0},
      { 1,  0,  0,  0,  0,  0,  1, -1,  0,  0,  0,  0,  0,  0},
      { 1,  0,  0,  0,  0,  0,  0,  1,  0, -1,  0,  0,  0,  0},
      { 0,  0,  0, -2,  0,  0,  2, -2,  0,  0,  0,  0,  0,  0},
      { 0,  0,  0, -2,  0,  0,  0,  1,  0, -1,  0,  0,  0,  0},
      { 0,  0,  2,  0,  2,  0, -2,  2,  0,  0,  0,  0,  0,  0},
      { 0,  0,  2,  0,  2,  0,  0, -1,  0,  1,  0,  0,  0,  0},
      { 0,  0,  2,  0,  2,  0, -1,  1,  0,  0,  0,  0,  0,  0},
      { 0,  0,  2,  0,  2,  0, -2,  3,  0,  0,  0,  0,  0,  0},
      { 0,  0,  0,  2,  0,  0,  0,  2,  0, -2,  0,  0,  0,  0},
      { 0,  0,  1,  1,  2,  0,  0,  1,  0,  0,  0,  0,  0,  0},
      { 1,  0,  2,  0,  2,  0,  0,  1,  0,  0,  0,  0,  0,  0},
      {-1,  0,  2,  0,  2,  0, 10, -3,  0,  0,  0,  0,  0,  0},
      { 0,  0,  1,  1,  1,  0,  0,  1,  0,  0,  0,  0,  0,  0},
      { 1,  0,  2,  0,  2,  0,  0,  1,  0,  0,  0,  0,  0,  0},
      { 0,  0,  2,  0,  2,  0,  0,  4, -8,  3,  0,  0,  0,  0},
      { 0,  0,  2,  0,  2,  0,  0, -4,  8, -3,  0,  0,  0,  0},
      {-1,  0,  2,  0,  2,  0,  0, -4,  8, -3,  0,  0,  0,  0},
      { 2,  0,  2, -2,  2,  0,  0, -2,  0,  3,  0,  0,  0,  0},
      { 1,  0,  2,  0,  1,  0,  0, -2,  0,  3,  0,  0,  0,  0},
      { 0,  0,  1,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0},
      {-1,  0,  2,  0,  1,  0,  0,  1,  0,  0,  0,  0,  0,  0},
      {-2,  0,  2,  2,  2,  0,  0,  2,  0, -2,  0,  0,  0,  0},
      { 0,  0,  2,  0,  2,  0,  2, -3,  0,  0,  0,  0,  0,  0},
      { 0,  0,  2,  0,  2,  0,  1, -1,  0,  0,  0,  0,  0,  0},
      { 0,  0,  2,  0,  2,  0,  0,  1,  0, -1,  0,  0,  0,  0},
      { 0,  0,  2,  0,  2,  0,  2, -2,  0,  0,  0,  0,  0,  0},
      {-1,  0,  2,  2,  2,  0,  0, -1,  0,  1,  0,  0,  0,  0},
      { 1,  0,  2,  0,  2,  0, -1,  1,  0,  0,  0,  0,  0,  0},
      {-1,  0,  2,  2,  2,  0,  0,  2,  0, -3,  0,  0,  0,  0},
      { 2,  0,  2,  0,  2,  0,  0,  2,  0, -3,  0,  0,  0,  0},
      { 1,  0,  2,  0,  2,  0,  0, -4,  8, -3,  0,  0,  0,  0},
      { 1,  0,  2,  0,  2,  0,  0,  4, -8,  3,  0,  0,  0,  0},
      { 1,  0,  1,  1,  1,  0,  0,  1,  0,  0,  0,  0,  0,  0},
      { 0,  0,  2,  0,  2,  0,  0,  1,  0,  0,  0,  0,  0,  0},
      { 2,  0,  2,  0,  1,  0,  0,  1,  0,  0,  0,  0,  0,  0},
      {-1,  0,  2,  2,  2,  0,  0,  2,  0, -2,  0,  0,  0,  0},
      {-1,  0,  2,  2,  2,  0,  3, -3,  0,  0,  0,  0,  0,  0},
      { 1,  0,  2,  0,  2,  0,  1, -1,  0,  0,  0,  0,  0,  0},
      { 0,  0,  2,  2,  2,  0,  0,  2,  0, -2,  0,  0,  0,  0}};

/*
   Planetary nutation coefficients, unit 1e-7 arcsec:
   longitude (sin, cos), obliquity (sin, cos)

   Each row of coefficients in 'cpl_t' belongs with the corresponding
   row of fundamental-argument multipliers in 'napl_t'.
*/

   static const double cpl_t[687][4] = {
      { 1440.0,          0.0,          0.0,          0.0},
      {   56.0,       -117.0,        -42.0,        -40.0},
      {  125.0,        -43.0,          0.0,        -54.0},
      {    0.0,          5.0,          0.0,          0.0},
      {    3.0,         -7.0,         -3.0,          0.0},
      {    3.0,          0.0,          0.0,         -2.0},
      { -114.0,          0.0,          0.0,         61.0},
      { -219.0,         89.0,          0.0,          0.0},
      {   -3.0,          0.0,          0.0,          0.0},
      { -462.0,       1604.0,          0.0,          0.0},
      {   99.0,          0.0,          0.0,        -53.0},
      {   -3.0,          0.0,          0.0,          2.0},
      {    0.0,          6.0,          2.0,          0.0},
      {    3.0,          0.0,          0.0,          0.0},
      {  -12.0,          0.0,          0.0,          0.0},
      {   14.0,       -218.0,        117.0,          8.0},
      {   31.0,       -481.0,       -257.0,        -17.0},
      { -491.0,        128.0,          0.0,          0.0},
      {-3084.0,       5123.0,       2735.0,       1647.0},
      {-1444.0,       2409.0,      -1286.0,       -771.0},
      {   11.0,        -24.0,        -11.0,         -9.0},
      {   26.0,         -9.0,          0.0,          0.0},
      {  103.0,        -60.0,          0.0,          0.0},
      {    0.0,        -13.0,         -7.0,          0.0},
      {  -26.0,        -29.0,        -16.0,         14.0},
      {    9.0,        -27.0,        -14.0,         -5.0},
      {   12.0,          0.0,          0.0,         -6.0},
      {   -7.0,          0.0,          0.0,          0.0},
      {    0.0,         24.0,          0.0,          0.0},
      {  284.0,          0.0,          0.0,       -151.0},
      {  226.0,        101.0,          0.0,          0.0},
      {    0.0,         -8.0,         -2.0,          0.0},
      {    0.0,         -6.0,         -3.0,          0.0},
      {    5.0,          0.0,          0.0,         -3.0},
      {  -41.0,        175.0,         76.0,         17.0},
      {    0.0,         15.0,          6.0,          0.0},
      {  425.0,        212.0,       -133.0,        269.0},
      { 1200.0,        598.0,        319.0,       -641.0},
      {  235.0,        334.0,          0.0,          0.0},
      {   11.0,        -12.0,         -7.0,         -6.0},
      {    5.0,         -6.0,          3.0,          3.0},
      {   -5.0,          0.0,          0.0,          3.0},
      {    6.0,          0.0,          0.0,         -3.0},
      {   15.0,          0.0,          0.0,          0.0},
      {   13.0,          0.0,          0.0,         -7.0},
      {   -6.0,         -9.0,          0.0,          0.0},
      {  266.0,        -78.0,          0.0,          0.0},
      { -460.0,       -435.0,       -232.0,        246.0},
      {    0.0,         15.0,          7.0,          0.0},
      {   -3.0,          0.0,          0.0,          2.0},
      {    0.0,        131.0,          0.0,          0.0},
      {    4.0,          0.0,          0.0,          0.0},
      {    0.0,          3.0,          0.0,          0.0},
      {    0.0,          4.0,          2.0,          0.0},
      {    0.0,          3.0,          0.0,          0.0},
      {  -17.0,        -19.0,        -10.0,          9.0},
      {   -9.0,        -11.0,          6.0,         -5.0},
      {   -6.0,          0.0,          0.0,          3.0},
      {  -16.0,          8.0,          0.0,          0.0},
      {    0.0,          3.0,          0.0,          0.0},
      {   11.0,         24.0,         11.0,         -5.0},
      {   -3.0,         -4.0,         -2.0,          1.0},
      {    3.0,          0.0,          0.0,         -1.0},
      {    0.0,         -8.0,         -4.0,          0.0},
      {    0.0,          3.0,          0.0,          0.0},
      {    0.0,          5.0,          0.0,          0.0},
      {    0.0,          3.0,          2.0,          0.0},
      {   -6.0,          4.0,          2.0,          3.0},
      {   -3.0,         -5.0,          0.0,          0.0},
      {   -5.0,          0.0,          0.0,          2.0},
      {    4.0,         24.0,         13.0,         -2.0},
      {  -42.0,         20.0,          0.0,          0.0},
      {  -10.0,        233.0,          0.0,          0.0},
      {   -3.0,          0.0,          0.0,          1.0},
      {   78.0,        -18.0,          0.0,          0.0},
      {    0.0,          3.0,          1.0,          0.0},
      {    0.0,         -3.0,         -1.0,          0.0},
      {    0.0,         -4.0,         -2.0,          1.0},
      {    0.0,         -8.0,         -4.0,         -1.0},
      {    0.0,         -5.0,          3.0,          0.0},
      {   -7.0,          0.0,          0.0,          3.0},
      {  -14.0,          8.0,          3.0,          6.0},
      {    0.0,          8.0,         -4.0,          0.0},
      {    0.0,         19.0,         10.0,          0.0},
      {   45.0,        -22.0,          0.0,          0.0},
      {   -3.0,          0.0,          0.0,          0.0},
      {    0.0,         -3.0,          0.0,          0.0},
      {    0.0,          3.0,          0.0,          0.0},
      {    3.0,          5.0,          3.0,         -2.0},
      {   89.0,        -16.0,         -9.0,        -48.0},
      {    0.0,          3.0,          0.0,          0.0},
      {   -3.0,          7.0,          4.0,          2.0},
      { -349.0,        -62.0,          0.0,          0.0},
      {  -15.0,         22.0,          0.0,          0.0},
      {   -3.0,          0.0,          0.0,          0.0},
      {  -53.0,          0.0,          0.0,          0.0},
      {    5.0,          0.0,          0.0,         -3.0},
      {    0.0,         -8.0,          0.0,          0.0},
      {   15.0,         -7.0,         -4.0,         -8.0},
      {   -3.0,          0.0,          0.0,          1.0},
      {  -21.0,        -78.0,          0.0,          0.0},
      {   20.0,        -70.0,        -37.0,        -11.0},
      {    0.0,          6.0,          3.0,          0.0},
      {    5.0,          3.0,          2.0,         -2.0},
      {  -17.0,         -4.0,         -2.0,          9.0},
      {    0.0,          6.0,          3.0,          0.0},
      {   32.0,         15.0,         -8.0,         17.0},
      {  174.0,         84.0,         45.0,        -93.0},
      {   11.0,         56.0,          0.0,          0.0},
      {  -66.0,        -12.0,         -6.0,         35.0},
      {   47.0,          8.0,          4.0,        -25.0},
      {    0.0,          8.0,          4.0,          0.0},
      {   10.0,        -22.0,        -12.0,         -5.0},
      {   -3.0,          0.0,          0.0,          2.0},
      {  -24.0,         12.0,          0.0,          0.0},
      {    5.0,         -6.0,          0.0,          0.0},
      {    3.0,          0.0,          0.0,         -2.0},
      {    4.0,          3.0,          1.0,         -2.0},
      {    0.0,         29.0,         15.0,          0.0},
      {   -5.0,         -4.0,         -2.0,          2.0},
      {    8.0,         -3.0,         -1.0,         -5.0},
      {    0.0,         -3.0,          0.0,          0.0},
      {   10.0,          0.0,          0.0,          0.0},
      {    3.0,          0.0,          0.0,         -2.0},
      {   -5.0,          0.0,          0.0,          3.0},
      {   46.0,         66.0,         35.0,        -25.0},
      {  -14.0,          7.0,          0.0,          0.0},
      {    0.0,          3.0,          2.0,          0.0},
      {   -5.0,          0.0,          0.0,          0.0},
      {  -68.0,        -34.0,        -18.0,         36.0},
      {    0.0,         14.0,          7.0,          0.0},
      {   10.0,         -6.0,         -3.0,         -5.0},
      {   -5.0,         -4.0,         -2.0,          3.0},
      {   -3.0,          5.0,          2.0,          1.0},
      {   76.0,         17.0,          9.0,        -41.0},
      {   84.0,        298.0,        159.0,        -45.0},
      {    3.0,          0.0,          0.0,         -1.0},
      {   -3.0,          0.0,          0.0,          2.0},
      {   -3.0,          0.0,          0.0,          1.0},
      {  -82.0,        292.0,        156.0,         44.0},
      {  -73.0,         17.0,          9.0,         39.0},
      {   -9.0,        -16.0,          0.0,          0.0},
      {    3.0,          0.0,         -1.0,         -2.0},
      {   -3.0,          0.0,          0.0,          0.0},
      {   -9.0,         -5.0,         -3.0,          5.0},
      { -439.0,          0.0,          0.0,          0.0},
      {   57.0,        -28.0,        -15.0,        -30.0},
      {    0.0,         -6.0,         -3.0,          0.0},
      {   -4.0,          0.0,          0.0,          2.0},
      {  -40.0,         57.0,         30.0,         21.0},
      {   23.0,          7.0,          3.0,        -13.0},
      {  273.0,         80.0,         43.0,       -146.0},
      { -449.0,        430.0,          0.0,          0.0},
      {   -8.0,        -47.0,        -25.0,          4.0},
      {    6.0,         47.0,         25.0,         -3.0},
      {    0.0,         23.0,         13.0,          0.0},
      {   -3.0,          0.0,          0.0,          2.0},
      {    3.0,         -4.0,         -2.0,         -2.0},
      {  -48.0,       -110.0,        -59.0,         26.0},
      {   51.0,        114.0,         61.0,        -27.0},
      { -133.0,          0.0,          0.0,         57.0},
      {    0.0,          4.0,          0.0,          0.0},
      {  -21.0,         -6.0,         -3.0,         11.0},
      {    0.0,         -3.0,         -1.0,          0.0},
      {  -11.0,        -21.0,        -11.0,          6.0},
      {  -18.0,       -436.0,       -233.0,          9.0},
      {   35.0,         -7.0,          0.0,          0.0},
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      {  -62.0,        -97.0,        -42.0,         27.0},
      {  -11.0,          5.0,          2.0,          5.0},
      {    0.0,        -19.0,         -8.0,          0.0},
      {   -3.0,          0.0,          0.0,          1.0},
      {    0.0,          4.0,          2.0,          0.0},
      {    0.0,          3.0,          0.0,          0.0},
      {    0.0,          4.0,          2.0,          0.0},
      {  -85.0,        -70.0,        -31.0,         37.0},
      {  163.0,        -12.0,         -5.0,        -72.0},
      {  -63.0,        -16.0,         -7.0,         28.0},
      {  -21.0,        -32.0,        -14.0,          9.0},
      {    0.0,         -3.0,         -1.0,          0.0},
      {    3.0,          0.0,          0.0,         -2.0},
      {    0.0,          8.0,          0.0,          0.0},
      {    3.0,         10.0,          4.0,         -1.0},
      {    3.0,          0.0,          0.0,         -1.0},
      {    0.0,         -7.0,         -3.0,          0.0},
      {    0.0,         -4.0,         -2.0,          0.0},
      {    6.0,         19.0,          0.0,          0.0},
      {    5.0,       -173.0,        -75.0,         -2.0},
      {    0.0,         -7.0,         -3.0,          0.0},
      {    7.0,        -12.0,         -5.0,         -3.0},
      {   -3.0,          0.0,          0.0,          2.0},
      {    3.0,         -4.0,         -2.0,         -1.0},
      {   74.0,          0.0,          0.0,        -32.0},
      {   -3.0,         12.0,          6.0,          2.0},
      {   26.0,        -14.0,         -6.0,        -11.0},
      {   19.0,          0.0,          0.0,         -8.0},
      {    6.0,         24.0,         13.0,         -3.0},
      {   83.0,          0.0,          0.0,          0.0},
      {    0.0,        -10.0,         -5.0,          0.0},
      {   11.0,         -3.0,         -1.0,         -5.0},
      {    3.0,          0.0,          1.0,         -1.0},
      {    3.0,          0.0,          0.0,         -1.0},
      {   -4.0,          0.0,          0.0,          0.0},
      {    5.0,        -23.0,        -12.0,         -3.0},
      { -339.0,          0.0,          0.0,        147.0},
      {    0.0,        -10.0,         -5.0,          0.0},
      {    5.0,          0.0,          0.0,          0.0},
      {    3.0,          0.0,          0.0,         -1.0},
      {    0.0,         -4.0,         -2.0,          0.0},
      {   18.0,         -3.0,          0.0,          0.0},
      {    9.0,        -11.0,         -5.0,         -4.0},
      {   -8.0,          0.0,          0.0,          4.0},
      {    3.0,          0.0,          0.0,         -1.0},
      {    0.0,          9.0,          0.0,          0.0},
      {    6.0,         -9.0,         -4.0,         -2.0},
      {   -4.0,        -12.0,          0.0,          0.0},
      {   67.0,        -91.0,        -39.0,        -29.0},
      {   30.0,        -18.0,         -8.0,        -13.0},
      {    0.0,          0.0,          0.0,          0.0},
      {    0.0,       -114.0,        -50.0,          0.0},
      {    0.0,          0.0,          0.0,         23.0},
      {  517.0,         16.0,          7.0,       -224.0},
      {    0.0,         -7.0,         -3.0,          0.0},
      {  143.0,         -3.0,         -1.0,        -62.0},
      {   29.0,          0.0,          0.0,        -13.0},
      {   -4.0,          0.0,          0.0,          2.0},
      {   -6.0,          0.0,          0.0,          3.0},
      {    5.0,         12.0,          5.0,         -2.0},
      {  -25.0,          0.0,          0.0,         11.0},
      {   -3.0,          0.0,          0.0,          1.0},
      {    0.0,          4.0,          2.0,          0.0},
      {  -22.0,         12.0,          5.0,         10.0},
      {   50.0,          0.0,          0.0,        -22.0},
      {    0.0,          7.0,          4.0,          0.0},
      {    0.0,          3.0,          1.0,          0.0},
      {   -4.0,          4.0,          2.0,          2.0},
      {   -5.0,        -11.0,         -5.0,          2.0},
      {    0.0,          4.0,          2.0,          0.0},
      {    4.0,         17.0,          9.0,         -2.0},
      {   59.0,          0.0,          0.0,          0.0},
      {    0.0,         -4.0,         -2.0,          0.0},
      {   -8.0,          0.0,          0.0,          4.0},
      {   -3.0,          0.0,          0.0,          0.0},
      {    4.0,        -15.0,         -8.0,         -2.0},
      {  370.0,         -8.0,          0.0,       -160.0},
      {    0.0,          0.0,         -3.0,          0.0},
      {    0.0,          3.0,          1.0,          0.0},
      {   -6.0,          3.0,          1.0,          3.0},
      {    0.0,          6.0,          0.0,          0.0},
      {  -10.0,          0.0,          0.0,          4.0},
      {    0.0,          9.0,          4.0,          0.0},
      {    4.0,         17.0,          7.0,         -2.0},
      {   34.0,          0.0,          0.0,        -15.0},
      {    0.0,          5.0,          3.0,          0.0},
      {   -5.0,          0.0,          0.0,          2.0},
      {  -37.0,         -7.0,         -3.0,         16.0},
      {    3.0,         13.0,          7.0,         -2.0},
      {   40.0,          0.0,          0.0,          0.0},
      {    0.0,         -3.0,         -2.0,          0.0},
      { -184.0,         -3.0,         -1.0,         80.0},
      {   -3.0,          0.0,          0.0,          1.0},
      {   -3.0,          0.0,          0.0,          0.0},
      {    0.0,        -10.0,         -6.0,         -1.0},
      {   31.0,         -6.0,          0.0,        -13.0},
      {   -3.0,        -32.0,        -14.0,          1.0},
      {   -7.0,          0.0,          0.0,          3.0},
      {    0.0,         -8.0,         -4.0,          0.0},
      {    3.0,         -4.0,          0.0,          0.0},
      {    0.0,          4.0,          0.0,          0.0},
      {    0.0,          3.0,          1.0,          0.0},
      {   19.0,        -23.0,        -10.0,          2.0},
      {    0.0,          0.0,          0.0,        -10.0},
      {    0.0,          3.0,          2.0,          0.0},
      {    0.0,          9.0,          5.0,         -1.0},
      {   28.0,          0.0,          0.0,          0.0},
      {    0.0,         -7.0,         -4.0,          0.0},
      {    8.0,         -4.0,          0.0,         -4.0},
      {    0.0,          0.0,         -2.0,          0.0},
      {    0.0,          3.0,          0.0,          0.0},
      {   -3.0,          0.0,          0.0,          1.0},
      {   -9.0,          0.0,          1.0,          4.0},
      {    3.0,         12.0,          5.0,         -1.0},
      {   17.0,         -3.0,         -1.0,          0.0},
      {    0.0,          7.0,          4.0,          0.0},
      {   19.0,          0.0,          0.0,          0.0},
      {    0.0,         -5.0,         -3.0,          0.0},
      {   14.0,         -3.0,          0.0,         -1.0},
      {    0.0,          0.0,         -1.0,          0.0},
      {    0.0,          0.0,          0.0,         -5.0},
      {    0.0,          5.0,          3.0,          0.0},
      {   13.0,          0.0,          0.0,          0.0},
      {    0.0,         -3.0,         -2.0,          0.0},
      {    2.0,          9.0,          4.0,          3.0},
      {    0.0,          0.0,          0.0,         -4.0},
      {    8.0,          0.0,          0.0,          0.0},
      {    0.0,          4.0,          2.0,          0.0},
      {    6.0,          0.0,          0.0,         -3.0},
      {    6.0,          0.0,          0.0,          0.0},
      {    0.0,          3.0,          1.0,          0.0},
      {    5.0,          0.0,          0.0,         -2.0},
      {    3.0,          0.0,          0.0,         -1.0},
      {   -3.0,          0.0,          0.0,          0.0},
      {    6.0,          0.0,          0.0,          0.0},
      {    7.0,          0.0,          0.0,          0.0},
      {   -4.0,          0.0,          0.0,          0.0},
      {    4.0,          0.0,          0.0,          0.0},
      {    6.0,          0.0,          0.0,          0.0},
      {    0.0,         -4.0,          0.0,          0.0},
      {    0.0,         -4.0,          0.0,          0.0},
      {    5.0,          0.0,          0.0,          0.0},
      {   -3.0,          0.0,          0.0,          0.0},
      {    4.0,          0.0,          0.0,          0.0},
      {   -5.0,          0.0,          0.0,          0.0},
      {    4.0,          0.0,          0.0,          0.0},
      {    0.0,          3.0,          0.0,          0.0},
      {   13.0,          0.0,          0.0,          0.0},
      {   21.0,         11.0,          0.0,          0.0},
      {    0.0,         -5.0,          0.0,          0.0},
      {    0.0,         -5.0,         -2.0,          0.0},
      {    0.0,          5.0,          3.0,          0.0},
      {    0.0,         -5.0,          0.0,          0.0},
      {   -3.0,          0.0,          0.0,          2.0},
      {   20.0,         10.0,          0.0,          0.0},
      {  -34.0,          0.0,          0.0,          0.0},
      {  -19.0,          0.0,          0.0,          0.0},
      {    3.0,          0.0,          0.0,         -2.0},
      {   -3.0,          0.0,          0.0,          1.0},
      {   -6.0,          0.0,          0.0,          3.0},
      {   -4.0,          0.0,          0.0,          0.0},
      {    3.0,          0.0,          0.0,          0.0},
      {    3.0,          0.0,          0.0,          0.0},
      {    4.0,          0.0,          0.0,          0.0},
      {    3.0,          0.0,          0.0,         -1.0},
      {    6.0,          0.0,          0.0,         -3.0},
      {   -8.0,          0.0,          0.0,          3.0},
      {    0.0,          3.0,          1.0,          0.0},
      {   -3.0,          0.0,          0.0,          0.0},
      {    0.0,         -3.0,         -2.0,          0.0},
      {  126.0,        -63.0,        -27.0,        -55.0},
      {   -5.0,          0.0,          1.0,          2.0},
      {   -3.0,         28.0,         15.0,          2.0},
      {    5.0,          0.0,          1.0,         -2.0},
      {    0.0,          9.0,          4.0,          1.0},
      {    0.0,          9.0,          4.0,         -1.0},
      { -126.0,        -63.0,        -27.0,         55.0},
      {    3.0,          0.0,          0.0,         -1.0},
      {   21.0,        -11.0,         -6.0,        -11.0},
      {    0.0,         -4.0,          0.0,          0.0},
      {  -21.0,        -11.0,         -6.0,         11.0},
      {   -3.0,          0.0,          0.0,          1.0},
      {    0.0,          3.0,          1.0,          0.0},
      {    8.0,          0.0,          0.0,         -4.0},
      {   -6.0,          0.0,          0.0,          3.0},
      {   -3.0,          0.0,          0.0,          1.0},
      {    3.0,          0.0,          0.0,         -1.0},
      {   -3.0,          0.0,          0.0,          1.0},
      {   -5.0,          0.0,          0.0,          2.0},
      {   24.0,        -12.0,         -5.0,        -11.0},
      {    0.0,          3.0,          1.0,          0.0},
      {    0.0,          3.0,          1.0,          0.0},
      {    0.0,          3.0,          2.0,          0.0},
      {  -24.0,        -12.0,         -5.0,         10.0},
      {    4.0,          0.0,         -1.0,         -2.0},
      {   13.0,          0.0,          0.0,         -6.0},
      {    7.0,          0.0,          0.0,         -3.0},
      {    3.0,          0.0,          0.0,         -1.0},
      {    3.0,          0.0,          0.0,         -1.0}};

/*
   Interval between fundamental epoch J2000.0 and given date.
*/

   t = ((jd_high - T0) + jd_low) / 36525.0;

/*
   Compute fundamental arguments from Simon et al. (1994), in radians.
*/

   fund_args (t, a);

/*
   ** Luni-solar nutation. **
*/

/*
   Initialize the nutation values.
*/

   dp = 0.0;
   de = 0.0;

/*
   Summation of luni-solar nutation series (in reverse order).
*/

   for (i = 677; i >= 0; i--)
   {

/*
   Argument and functions.
*/

      arg = fmod ((double) nals_t[i][0] * a[0]  +
                  (double) nals_t[i][1] * a[1]  +
                  (double) nals_t[i][2] * a[2]  +
                  (double) nals_t[i][3] * a[3]  +
                  (double) nals_t[i][4] * a[4], TWOPI);

      sarg = sin (arg);
      carg = cos (arg);

/*
   Term.
*/

      dp += (cls_t[i][0] + cls_t[i][1] * t) * sarg
              +   cls_t[i][2] * carg;
      de += (cls_t[i][3] + cls_t[i][4] * t) * carg
              +   cls_t[i][5] * sarg;
   }

/*
   Convert from 0.1 microarcsec units to radians.
*/

   factor = 1.0e-7 * ASEC2RAD;
   dpsils = dp * factor;
   depsls = de * factor;

/*
   ** Planetary nutation. **
*/

/*
   Mean anomaly of the Moon.
*/

   al = fmod (2.35555598 + 8328.6914269554 * t, TWOPI);

/*
   Mean anomaly of the Sun.
*/

   alsu = fmod (6.24006013 + 628.301955 * t, TWOPI);

/*
   Mean argument of the latitude of the Moon.
*/

   af = fmod (1.627905234 + 8433.466158131 * t, TWOPI);

/*
   Mean elongation of the Moon from the Sun.
*/

   ad = fmod (5.198466741 + 7771.3771468121 * t, TWOPI);

/*
   Mean longitude of the ascending node of the Moon.
*/

   aom = fmod (2.18243920 - 33.757045 * t, TWOPI);

/*
   General accumulated precession in longitude.
*/

   apa = (0.02438175 + 0.00000538691 * t) * t;
/*
   Planetary longitudes, Mercury through Neptune (Souchay et al. 1999).
*/

   alme = fmod (4.402608842 + 2608.7903141574 * t, TWOPI);
   alve = fmod (3.176146697 + 1021.3285546211 * t, TWOPI);
   alea = fmod (1.753470314 +  628.3075849991 * t, TWOPI);
   alma = fmod (6.203480913 +  334.0612426700 * t, TWOPI);
   alju = fmod (0.599546497 +   52.9690962641 * t, TWOPI);
   alsa = fmod (0.874016757 +   21.3299104960 * t, TWOPI);
   alur = fmod (5.481293871 +    7.4781598567 * t, TWOPI);
   alne = fmod (5.321159000 +    3.8127774000 * t, TWOPI);

/*
   Initialize the nutation values.
*/

   dp = 0.0;
   de = 0.0;

/*
   Summation of planetary nutation series (in reverse order).
*/

   for (i = 686; i >= 0; i--)
   {

/*
   Argument and functions.
*/

      arg = fmod ((double) napl_t[i][ 0] * al    +
                  (double) napl_t[i][ 1] * alsu  +
                  (double) napl_t[i][ 2] * af    +
                  (double) napl_t[i][ 3] * ad    +
                  (double) napl_t[i][ 4] * aom   +
                  (double) napl_t[i][ 5] * alme  +
                  (double) napl_t[i][ 6] * alve  +
                  (double) napl_t[i][ 7] * alea  +
                  (double) napl_t[i][ 8] * alma  +
                  (double) napl_t[i][ 9] * alju  +
                  (double) napl_t[i][10] * alsa  +
                  (double) napl_t[i][11] * alur  +
                  (double) napl_t[i][12] * alne  +
                  (double) napl_t[i][13] * apa, TWOPI);

      sarg = sin (arg);
      carg = cos (arg);

/*
   Term.
*/

      dp += cpl_t[i][0] * sarg + cpl_t[i][1] * carg;
      de += cpl_t[i][2] * sarg + cpl_t[i][3] * carg;
   }

   dpsipl = dp * factor;
   depspl = de * factor;

/*
   Total: Add planetary and luni-solar components.
*/

   *dpsi = dpsipl + dpsils;
   *deps = depspl + depsls;

   return;
}
